Lesson 26 Hormework 5. Sean's mother bought \( \frac{3}{4} \mathrm{lb} \) of Gouda cheese and \( \frac{1}{3} \mathrm{lb} \) less of cheddar cheese. How many pounds of cheese did she buy altogether?

To find the total pounds of cheese Sean's mother bought, first, we need to calculate the weight of the cheddar cheese. Since she bought \( \frac{1}{3} \) lb less than Gouda, we subtract \( \frac{1}{3} \) lb from \( \frac{3}{4} \) lb. We can convert \( \frac{3}{4} \) to have a common denominator with \( \frac{1}{3} \) which is 12: \[ \frac{3}{4} = \frac{9}{12} \quad \text{and} \quad \frac{1}{3} = \frac{4}{12} \] Now subtract the two: \[ \frac{9}{12} - \frac{4}{12} = \frac{5}{12} \text{ lb of cheddar cheese} \] Now, add the weights of both cheeses together: \[ \frac{3}{4} + \frac{5}{12} \] Converting \( \frac{3}{4} \) to twelfths gives: \[ \frac{3}{4} = \frac{9}{12} \] Now add: \[ \frac{9}{12} + \frac{5}{12} = \frac{14}{12} = \frac{7}{6} \text{ lb} \] So, Sean's mother bought \( \frac{7}{6} \) pounds of cheese altogether. That's 1 and \( \frac{1}{6} \) pounds of cheesy goodness!